Thermal explosion, times to ignition and near-critical behaviour in uniform-temperature systems. Part 4.—Effects of programmed ambient temperature

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Abstract
When a deceleratory exothermic reaction proceeds in a closed vessel under conditions of varying ambient temperature, thermal runaway to explosive speeds may occur. The course of events is determined by the rate of change of ambient temperature, the responsiveness of the reaction rate to both temperature and extent of reaction, and the maximum possible extent of self-heating. The problem is investigated systematically, though not by employing ‘large activation energy’ asymptotics. We give a very general analysis for any temperature and concentration dependence (not merely mth-order Arrhenius). The primitive model which neglects reactant consumption and uses a fixed ambient temperature is seen to be important in understanding the full problem. The critical conditions are then expressed in terms of shifts in the Semenov number (Se or ψ) from the primitive value. The treatment also deals with whether it is possible to prevent an ignition in a normally supercritical reaction by external cooling. Times to ignition, or to reach maximum temperature for a subcritical reaction, are given as simple but general formulae for both external heating and cooling.

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